Ask a dozen military historians to name the single most pivotal battle or campaign of World War II—the one operation that saw the war’s momentum irrevocably swing from the Axis to the Allied powers — and you’ll get a dozen answers. Did the pendulum shift as early as the Battle of Britain? At Midway? During the liberation of Paris? Kursk? The Battle of the Bulge? Stalingrad? The varieties of ways one might conceivably measure momentum, from the numbers of casualties sustained (or inflicted) to the more esoteric notion of “troop morale,” makes a definitive answer impossible.

But one campaign that everyone agrees was a significant turning point in the Allied effort was launched more than 70 years ago, in July 1943. Before dawn on July 10 of that year, 150,000 American and British troops—along with Canadian, Free French and other Allies, and 3,000 ships, 600 tanks and 4,000 aircraft—made for the southern shores of the largest island in the Mediterranean Sea: the storied, 10,000-square-mile land of Sicily. Within six weeks, the Allies had pushed Axis troops (primarily Germans) out of Sicily and were poised for the invasion of mainland Italy and one of the most arduous 20 months of the entire war: the long, often brutal Italian Campaign.

Tens of thousands of troops, on both sides, were killed or listed as missing, while hundreds of thousands more were wounded. And, of course—as in most every major campaign of the war—hundreds of thousands of civilians were killed, while countless more were wounded, raped, left homeless and otherwise traumatized.

Here, LIFE.com presents a series of both rare and classic color pictures made throughout the Italian Campaign by the great Carl Mydans.

Finally, it’s worth noting that, within weeks of the start of the invasion of Sicily, the Fascist dictator Benito Mussolini, who had ruled Italy for more than two decades, was booted from power and arrested. “Il Duce” subsequently escaped, with German help, and was then on the run or in hiding without cease for almost two years. He was captured by Italian partisans in late April 1945, summarily executed, and—along with his mistress and several other Fascists—literally hanged by his heels, in public, for all to see.